Theory of Ferroelectric ZrO₂ Monolayers on Si

Abstract

We use density functional theory and Monte Carlo lattice simulations to investigate the structure of ZrO2 monolayers on Si(001). Recently, we have reported on the experimental growth of amorphous ZrO2 monolayers on silicon and their ferroelectric properties, marking the achievement of the thinnest possible ferroelectric oxide [M. Dogan et al. Nano Lett., 18 (1) (2018) [1]]. Here, we first describe the rich landscape of atomic configurations of monocrystalline ZrO2 monolayers on Si and determine the local energy minima. Because of the multitude of low-energy configurations we find, we consider the coexistence of finite-sized regions of different configurations. We create a simple nearest-neighbor lattice model with parameters extracted from DFT calculations, and solve it numerically using a cluster Monte Carlo algorithm. Our results suggest that up to room temperature, the ZrO2 monolayer consists of small domains of two low-energy configurations with opposite ferroelectric polarization. This explains the observed ferroelectric behavior in the experimental films as a collection of crystalline regions, which are a few nanometers in size, being switched with the application of an external electric field.

Epitaxial ferroelectric interfacial devices

“…379,[400][401][402] A related ferroelectric that has been recently discovered is monolayer ZrO 2 grown on silicon. 403,404 One of the stable crystal structures of ZrO 2 is the fluorite structure, in which an individual atomic ZrO 2 plane in the material is polar. In the bulk, this polarization is not switchable, but a combination of first principles calculations and experiment shows that a single ZrO 2 plane grown atomically abruptly on silicon has two stable structures with different polarizations.…”

Electron beam-induced nanopores in Bernal-stacked hexagonal boron nitride

“…In the usual Metropolis algorithm for the Heisenberg model, at each simulation step, an attempt is made to randomize one of the spins [54]. However, this leads to a critical slowing down where the decorrelation time diverges near the crit-ical temperature [55,56], which in this case is 0 K. To overcome this problem to some degree, instead of choosing the proposed direction of the spin at random, we choose it according to the formula ∆θ = cos −1 K −1 log(exp(−K) + 2r sinh(K)) , (2) where ∆θ is the angle between the new spin and the old spin, K = (J1+J2) /(k B T ) and r is a random number between 0 and 1 [57]. This attempt is then accepted or rejected based on the Boltzmann factor of the energy difference between the proposed and original configurations, which generates a sampling of the configuration space that obeys the detailed balance condition [56].…”

Frustration and Atomic Ordering in a Monolayer Semiconductor Alloy

“…If all the triangles have at least (and only) one pair of parallel spins, the energy is minimized. To explore the thermodynamics of species distribution at finite temperature in the alloys, we solve a nearest-neighbor model using Monte Carlo simulations [21,22]. [1,23].…”